Problem 388Published on Saturday, 9th June 2012, 02:00 pm; Solved by 334; Difficulty rating: 50%
Consider all lattice points (a,b,c) with 0 ≤ a,b,c ≤ N.
From the origin O(0,0,0) all lines are drawn to the other lattice points.
Let D(N) be the number of distinct such lines.
You are given that D(1 000 000) = 831909254469114121.
Find D(1010). Give as your answer the first nine digits followed by the last nine digits.